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Popular >

extreme f(x)=(x^2-7)(x^2-6)(x^2+4)

Solution

extreme points

f (x) = (x^{2} - 7) (x^{2} - 6) (x^{2} + 4)

Solution

Minimum - \frac{9 + 111}{3}, \frac{- 200 111 - 1890}{9} + 294 + 14111, Maximum (0, 168), Minimum \frac{9 + 111}{3}, \frac{- 200 111 - 1890}{9} + 294 + 14111

Solution steps

f^{'} (x) = 2 x (3 x^{4} - 18 x^{2} - 10)

Find intervals:

Decreasing

: - \infty < x < - \frac{9 + 111}{3},

Increasing

: - \frac{9 + 111}{3} < x < 0,

Decreasing

: 0 < x < \frac{9 + 111}{3},

Increasing

: \frac{9 + 111}{3} < x < \infty

Plug

x = - \frac{9 + 111}{3}

into

(x^{2} - 7) (x^{2} - 6) (x^{2} + 4) : \frac{- 200 111 - 1890}{9} + 294 + 14111

Minimum - \frac{9 + 111}{3}, \frac{- 200 111 - 1890}{9} + 294 + 14111

Plug

x = 0

into

(x^{2} - 7) (x^{2} - 6) (x^{2} + 4) : 168

Maximum (0, 168)

Plug

x = \frac{9 + 111}{3}

into

(x^{2} - 7) (x^{2} - 6) (x^{2} + 4) : \frac{- 200 111 - 1890}{9} + 294 + 14111

Minimum \frac{9 + 111}{3}, \frac{- 200 111 - 1890}{9} + 294 + 14111

Minimum - \frac{9 + 111}{3}, \frac{- 200 111 - 1890}{9} + 294 + 14111, Maximum (0, 168), Minimum \frac{9 + 111}{3}, \frac{- 200 111 - 1890}{9} + 294 + 14111

Popular Examples

extreme f(x)=(x-3)^{4/3},-7<= x<= 7 extreme points

f (x) = (x - 3)^{\frac{4}{3}}, - 7 \leq x \leq 7

extreme 2x^3-2x^2-x-9 extreme points

2 x^{3} - 2 x^{2} - x - 9

extreme y=(x^2)/2-3x+7/2 extreme points

y = \frac{x ^{2}}{2} - 3 x + \frac{7}{2}

extreme P(x,y)=-4x+5y-x^2+2xy-7y^2+9 extreme points

P (x, y) = - 4 x + 5 y - x^{2} + 2 x y - 7 y^{2} + 9

extreme f(x)=2x^2+5(7-x)^2 extreme points

f (x) = 2 x^{2} + 5 (7 - x)^{2}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^2-7)(x^2-6)(x^2+4) ?
The extreme f(x)=(x^2-7)(x^2-6)(x^2+4) is